Gen question about watts vs range

Im no scientist and have not tested this situation so this is off the top of my head but I would say no difference. All things being equal (and they never are) you bike will behave exactly the same.

If you have more power available you will probably use it to climb up that hill a little easier or go a little fast through that intersection. So you will probably use more amps.

I would think to do the exact same amount of work it would require the same amount of energy give your statement. Very unknowledgeable reply sorry I can't do better.

In your example it would depend on the controller, the math is volts x amps = watts
So 36 x 13.89 = 500 which means your controller will deliver roughly 14 amps.
And 36 x 19.44 = 700 which means your controller will deliver roughly 20 amps.
There should really be no difference in range between the two; the 700 watt setup would just be a little quicker.

Your range is governed more by the battery pack chemistry and amp-hour rating.
36 volts worth of 10 amp-hour lead acid batteries means that theoretically you could draw 10 amps for one hour on the pack, but seeing as how the rule of thumb is to never run the lead acid pack below 50% capacity* you would really only get 10 amps for ~ 30 mins.

So if you want to run your 700 watt setup with 10 amp-hour batteries and your controller is drawing roughly 20 amps and you don't want to run the pack below 50% capacity, you are looking at about 15 minutes continuous runtime, and I'm guessing that your motor/controller combo gets your bike a top speed of 20 mph max, so your range on a 10 amp-hour lead acid pack is realistically ~ 5 miles.

Go with lithium and you may get 10 miles or more.

* running a lead acid pack below 50% capacity will affect the number of recycles or how many time it can be recharged to capacity. If you stick with the 50% rule you may get 300 or more recycles out of your pack, but run it down to 10% and you will get maybe 50 recycles or maybe less.

I am by no means a scientist either, and the above information is based solely on my own personal experience.

I find it fairly easy to stay above the min charge on an sla, as they become very close to useless at around 12.1v. The 11.50 minimum they recommend per battery won't even run the controller. Even without one, the motor isn't pulling much at all, so you would want to recharge them anyway.

I have never tried lithium but I am saving up for new batteries when these die. i will be trying something different for sure. I'm hoping by the time I save the money, batteries have come down. I might just buy nimh cells with soldier tabs and make my own. The best info I find says they don't need fancy circuitry. I charge mine in 12v pieces anyway and that would work I think. If I read it right.

It looks as though I can make a 24v 10ah pack for a hundred bucks, give or take. The advantage for me is that I could replace a single cell without too much trouble. With a little luck that would prolong the life of the pack. I expect that I would string two 10ah together to get 20ah for 200 bucks. I'm still checking it out though.

As a test I might build just one as 12 20ah and run it with a sla to make up 24v 20ah and just compare how they hold up side by side.